Through the use of reasoning, students learn that mathematics makes sense. -National Council of Teachers of Mathematics
Instructional programs from prekindergarten through grade 12 should enable all students to:
• Recognize reasoning and proof as fundamental aspects of mathematics; make and investigate mathematical conjectures;
• Develop and evaluate mathematical arguments and proofs; and
• Select and use various types of reasoning and methods of proof.
Grade Ten
Characteristics and Properties:
3. Make, test and establish the validity of conjectures about geometric properties and relationships using counterexample, inductive and deductive reasoning, and paragraph or two-column proof, including:
a. prove the Pythagorean Theorem;
b. prove theorems involving triangle similarity and congruence;
c. prove theorems involving properties of lines, angles, triangles and quadrilaterals;
d. test a conjecture using basic constructions made with a compass and straightedge or technology.
By the end of the 11-12 program
D. Select and use various types of reasoning and methods of proof.
E. Evaluate a mathematical argument and use reasoning and logic to judge its validity.
F. Present complete and convincing arguments and justifications, using inductive and deductive reasoning, adapted to be effective for various audiences.
G. Understand the difference between a statement that is verified by mathematical proof, such as a theorem, and one that is verified empirically using examples or data.
Reasoning and Proof Standard
Through the use of reasoning, students learn that mathematics makes sense. -National Council of Teachers of Mathematics
Instructional programs from prekindergarten through grade 12 should enable all students to:
• Recognize reasoning and proof as fundamental aspects of mathematics; make and investigate mathematical conjectures;
• Develop and evaluate mathematical arguments and proofs; and
• Select and use various types of reasoning and methods of proof.
Grade Ten
Characteristics and Properties:
3. Make, test and establish the validity of conjectures about geometric properties and relationships using counterexample, inductive and deductive reasoning, and paragraph or two-column proof, including:
a. prove the Pythagorean Theorem;
b. prove theorems involving triangle similarity and congruence;
c. prove theorems involving properties of lines, angles, triangles and quadrilaterals;
d. test a conjecture using basic constructions made with a compass and straightedge or technology.
By the end of the 11-12 program
D. Select and use various types of reasoning and methods of proof.
E. Evaluate a mathematical argument and use reasoning and logic to judge its validity.
F. Present complete and convincing arguments and justifications, using inductive and deductive reasoning, adapted to be effective for various audiences.
G. Understand the difference between a statement that is verified by mathematical proof, such as a theorem, and one that is verified empirically using examples or data.